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3 years ago

The matrix 1 2 4(0 1 6/7 is being used to solve a system of equations. The solution to the system is

1 answer:

5 0

| 1 2 ||x| = |4| - | 3 -1 ||y| |6| -3 | 1 2||x| = |4| 
| 3 -1||y| |6| 

|-3 -6||x| = |-12| 
| 3 -1||y| |6 | 

| 0 -7 ||x| = | -6 | 
| 3 -1 ||y| | 6 | 

y = 6/7 

x = 16/7

You might be interested in

Solve with all work −4(2 + 9) + 3 = 6 − 4( − 3)

ra1l [238]

Answer:

They do not equal eachother

Step-by-step explanation:

-4(2+9) + 3 = 6 - 4(-3)

-12 - 36 + 3 = 6 + 12

-45 = 18

3 0

2 years ago

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 10

WINSTONCH [101]

Answer:

The function for the outside temperature is represented by $T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$ , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

$A = \frac{100\º-70\º}{2}$

$A = 15\º$

Mean temperature

$\bar T = \frac{70\º+100\º}{2}$

$\bar T = 85\º$

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

$T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]$

Where:

$\bar T$ - Mean temperature, measured in degrees.

$A$ - Amplitude, measured in degrees.

$\tau$ - Daily period, measured in hours.

$t$ - Time, measured in hours. (where t = 0 corresponds with 5 AM).

If $\bar T = 85\º$ , $A = 15\º$ and $\tau = 24\,h$ , the resulting function for the outside temperature is:

$T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$

3 0

2 years ago

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var

Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5$

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{3765 - 3639}{59.5}$

$Z = 2.12$

$Z = 2.12$ has a pvalue of 0.983

X = 3513

$Z = \frac{X - \mu}{s}$

$Z = \frac{3513 - 3639}{59.5}$

$Z = -2.12$

$Z = -2.12$ has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0

3 years ago

Mariah has some toy horses. 18 of her toy horses are brown. The other toy horses are not brown. She has 39 toy horses in all. Ho

choli [55]

Answer:

21 of them aren't brown

How 2 solve:

Subtract

39-18= 21

5 0

2 years ago

Credit card cash advance borrow: $300 rate: 18% per year time: 6 months-,5 300 6

olga nikolaevna [1]

Answer:

Assuming the question is how much interest you will pay in the given time frame with the given terms.

Step-by-step explanation:

Borrowed $300

18% per yr = 18/12 = 1.5% per month

You borrowed for 6 months so you will end up paying 1.5%*6 =9% in interest

$300*(9% or 0.09) = $27 in interest paid + $300 in principal paid if paid off in 6 months.

Total $327.

If this was an economics class you would also have to factor in the depreciation of the principal amount month to month with minimum payments but I am guessing this is just a basic question so the above answer is correct enough.

7 0

2 years ago